Suggestions for OP based on my story below:
Definitely get new, whole, 6000 springs as stated above. Consider upgrading the axle tube wall thickness as RV industry uses the lightest, cheapest, wall thickness (3” tube comes in 3 thicknesses from Dexter.) If the hub is actually the same for 6000 lb consider using 7000 lb backing plate if you are having any lack of trailer brake effort. X2 on wet bolts and heavy links. If the trailer uses 10” I beams in the frame, I would not worry about carrying more weight. You might compare your trailer to the closest current model to see what the current GVWR is.
My story:
We ordered a Coachman Chaparral 336TSIK in the spring of 2019. At that time the 2020 models used 5100 lb axles for the 4 “Lite” models and the two shortest “mid-profile” models (including our 336TSIK.) The 6 heavier, longer, trailers all used 7000 lb axles. Of the 12 models ours was rated the lowest of cargo capacity at 1480 (12,000 gross – 10,520 unloaded.) I asked the dealer to see if the factory would put on 6,000 lb axles. The answer was they can’t because all trailers must be manufactured standard per NHTSA. I took the trailer straight from the dealer to the axle shop via a CAT scale. The CAT showed empty weight of 10,780 leaving 1,220 for cargo, which is totally ridiculous for a 37’ fifth wheel trailer. So, I had the axle shop install Dexter 6,000 lb axles with Kodiak 6,000 lb disk brakes. For the 2022 model year Coachmen started putting 7,000 lb axles on the 336TSIK increasing GVWR to 13,500. Curious, I contacted engineering with my VIN to ask if they also upgraded the frame from mine—answer was no change to frame, just the axles. I also upgraded the tires from stock 235/80R16 to 235/85R16 to get the additional weight rating. We load pretty heavy—on last check we were a little over 13,500.